Vita e Pensiero

Keywords: Regime Switching Model, Hydroplants, Electricity forward Contracts, Stochastic Programming.

Keywords: Transmission Expansion Planning, Power Producer, Bilevel Programming.

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We propose a generalization of the three-parameters Zenga distribution obtaining a four-parameters model. The generalization is performed using the confluent hypergeometric distribution as mixing distributions in place of the classical beta. We compare the flexibility of the resulting model with that of the Zenga distribution observing some improvements.

The paper proposes a three-term decomposition of Zenga’s new inequality index over time. Given an initial and a final time, the link among inequality trend, re-ranking, and income growth is explained by decomposing the inequality index at the final time into three components: one measuring the effect of re-ranking between individuals, a second term gauging the effect of disproportional growth between individuals’ incomes, and a third component measuring the impact of the inequality existing at the initial time. The decomposition allows one to distinguish the determinants of inequality change from the contribution of the inequality at the initial time to the inequality at the final time. We applied the decomposition to Italian household income data collected by the Survey on Household Income and Wealth of the Bank of Italy, waves 2008-2010.

In this paper Zenga’s distribution is applied to 114 household incomes distributions from a panel survey conducted by Eurostat. Previous works showed the good behaviour of the model to describe income distributions and analyzed the possibility to impose restrictions on the parametric space so that the fitted models comply with some characteristics of interest of the samples. This work is the first application of the model on a wide number of distributions, showing that it can be used to describe incomes distributions of several countries. Maximum likelihood method on grouped data and methods based on the minimization of three different goodness of fit indexes are used to estimate parameters. The restriction that imposes the equivalence between the sample mean and the expected value of the fitted model is also considered. It results that the restriction should be used and the changes in fitting are analyzed in order to suggest which estimation method use jointly to the restriction. A final section is devoted to the direct proof that Zenga’s distribution has Paretian right-tail.